arXiv subjects

Joerg Schumacher

Publications and source records attributed to Joerg Schumacher.

58 records · Page 4Linked to original sources

arXiv1999

Three-dimensional spontaneous magnetic reconnection in neutral current sheets

Magnetic reconnection in an antiparallel uniform Harris current sheet equilibrium, which is initially perturbed by a region of enhanced resistivity limited in all three dimensions, is investigated through compressible magnetohydrodynamic simulations. Variable resistivity, coupled to the dynamics of the plasma by an electron-ion drift velocity criterion, is used during the evolution. A phase of magnetic reconnection amplifying with time and leading to eruptive energy release is triggered only if the initial perturbation is strongly elongated in the direction of current flow or if the threshold for the onset of anomalous resistivity is significantly lower than in the corresponding two-dimensional case. A Petschek-like configuration is then built up for \sim 100 Alfven times, but remains localized in the third dimension. Subsequently, a change of topology to an O-line at the center of the system (``secondary tearing'') occurs. This leads to enhanced and time-variable reconnection, to a second pair of outflow jets directed along the O-line, and to expansion of the reconnection process into the third dimension. High parallel current density components are created mainly near the region of enhanced resistivity.

astro-ph↗

arXiv1999

Bifurcation analysis of the plane sheet pinch

A numerical bifurcation analysis of the electrically driven plane sheet pinch is presented. The electrical conductivity varies across the sheet such as to allow instability of the quiescent basic state at some critical Hartmann number. The most unstable perturbation is the two-dimensional tearing mode. Restricting the whole problem to two spatial dimensions, this mode is followed up to a time-asymptotic steady state, which proves to be sensitive to three-dimensional perturbations even close to the point where the primary instability sets in. A comprehensive three-dimensional stability analysis of the two-dimensional steady tearing-mode state is performed by varying parameters of the sheet pinch. The instability with respect to three-dimensional perturbations is suppressed by a sufficiently strong magnetic field in the invariant direction of the equilibrium. For a special choice of the system parameters, the unstably perturbed state is followed up in its nonlinear evolution and is found to approach a three-dimensional steady state.

chao-dyn↗

arXiv1999

Magnetic field correlations in kinematic two-dimensional magnetohydrodynamic turbulence

The scaling properties of the second order magnetic structure function D_2^{(B)}(r) and the corresponding magnetic correlation function C_2^{(B)}(r) are derived for two-dimensional magnetohydrodynamic turbulence in the kinematic regime where the ratio of kinetic energy to magnetic energy is much larger than one. In this regime the magnetic flux function $ψ$ can be treated as a passive scalar advected in a two-dimensional turbulent flow. Its structure function $D_2^{(ψ)}(r)$ and the one for the magnetic field D_2^{(B)}(r) are connected by an exact relation. We calculate D_2^{(ψ)}(r) and thus D_2^{(B)}(r) within geometric measure theory over a wide range of scales r and magnetic Prandtl numbers Pr_m. The magnetic field correlations follow a r^{-4/3} - scaling law and show an anticorrelation at the beginning of the Batchelor regime indicative of the formation of strongly filamented current sheets. Differences to the full dynamic regime, where the ratio of kinetic to magnetic energies is smaller than in the kinematic case, are discussed.

chao-dyn↗

arXiv1999

Structure function of passive scalars in two-dimensional turbulence

The structure function of a scalar $θ({\bf x},t)$, passively advected in a two-dimensional turbulent flow ${\bf u}({\bf x},t)$, is discussed by means of the fractal dimension $δ^{(1)}_g$ of the passive scalar graph. A relation between $δ^{(1)}_g$, the scaling exponent $ζ_1^{(θ)}$ of the scalar structure function $D_1^{(θ)}(r)$, and the structure function D_2(r) of the underlying flow field is derived. Different from the 3-d case, the 2-d structure function also depends on an additional parameter, characteristic of the driving of the passive scalar. In the enstrophy inertial subrange a mean field approximation for the velocity structure function gives a scaling of the passive scalar graph with $δ^{(1)}_g<2$ for intermediate and large values of the Prandtl number Pr. In the energy inertial subrange a model for the energy spectrum and thus D_2(r) gives a passive scalar graph scaling with exponent $δ^{(1)}_g={5/3}$. Finally, we discuss an application to recent observations of scalar dispersion in non-universal 2-d flows.

chao-dyn↗